What is the integral of (sqrt(x)-x)/(x^2) ?

The integral of (sqrt(x)-x)/(x^2) is -2/(sqrt(x))-ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(x)-x)/(x^2)

\int \frac{x - x}{x ^{2}} d x

- \frac{2}{x} - ln ∣ x ∣ + C

Solution steps

\int \frac{x - x}{x ^{2}} d x

\frac{x - x}{x ^{2}} = (\frac{x}{x ^{2}} - \frac{x}{x ^{2}})

= \int \frac{x}{x ^{2}} - \frac{x}{x ^{2}} d x

Simplify

\frac{x}{x ^{2}} - \frac{x}{x ^{2}} : \frac{1}{x ^{\frac{3}{2}}} - \frac{1}{x}

= \int \frac{1}{x ^{\frac{3}{2}}} - \frac{1}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x ^{\frac{3}{2}}} d x - \int \frac{1}{x} d x

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{2}{x} - ln ∣ x ∣

Add a constant to the solution

= - \frac{2}{x} - ln ∣ x ∣ + C

\int x^{3} + 3 x^{2} d x

\int csc (x) - sin (x) d x

\int \frac{1}{x ^{2} + 12} d x

\int \frac{cos ( 6 x )}{x} d x

What is the integral of (sqrt(x)-x)/(x^2) ?
The integral of (sqrt(x)-x)/(x^2) is -2/(sqrt(x))-ln|x|+C